Higher dimensional Lax pairs of lower dimensional chaos and turbulence systems

Details Higher dimensional Lax pairs of lower dimensional chaos and turbulence systems Higher dimensional Lax pairs of lower dimensional chaos and turbulence systems

2001-07-12

arxiv.org/abs/nlin/0107028v1

Nonlinear Sciences

Pattern Formation and Solitons

8 pages

Scientific paper

In this letter, a definition of the higher dimensional Lax pair for a lower dimensional system which may be a chaotic system is given. A special concrete (2+1)-dimensional Lax pair for a general (1+1)-dimensional three order autonomous partial differential equation is studied. The result shows that any (1+1)-dimensional three order semi-linear autonomous system (no matter it is integrable or not) possesses infinitely many (2+1)-dimensional Lax pairs. Especially, every solution of the KdV equation and the Harry-Dym equation with their space variable being replaced by the field variable can be used to obtain a (2+1)-dimensional Lax pair of any three order (1+1)-dimensional semi-linear equation.

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